Measurements have been made of the thermal boundary resistance between liquid helium 11 and copper, lead and quartz, also between copper and liquid helium 11 at different densities. It is found that the dependence of the heat flow on the density of the helium is markedly different from that predicted by Khalatnikov (1952). According to this author, the transfer of heat from the solid surface to the helium takes place by the radiation of phonons, rather as would be the case between two dielectric solids. However, Khalatnikov does not take account of the fact that the layer of helium close to the solid has a much higher density than the bulk liquid. An analysis has been made of the effect of this dense layer, and the dependence of the heat flow on the density of the bulk helium found to be much closer to that observed experimentally. The experimental results using different solid materials suggest that, in metals at least, some other mechanism of heat transfer may be involved.